To proceed further with a concrete example we selected the Brusselator reaction system [1]}, [2]}. This is
a nonlinear model defined by \(f(u,v)=1-(b+1)u+c u^2v\)  and \(g(u,v)=bu-cu^2v\) , where \(b\)  and \(c\)  act as tunable parameters. In Fig. REF  we report the results for a choice of the model parameters giving rise to Turing patterns (\(b = 4\) , \(c = 6\) , \(D_u = 0.02\)  and \(D_v= 0.17\) ) and the same hypergraph previously used in Figs. REF  and REF . The dispersion relation (panel a) is clearly positive for a selection of \(\Lambda _H^{(\alpha )}\)  (red points). The
homogeneous solution becomes hence unstable and the ensuing patterns are displayed in panels b) and c).
<FIGURE>